Construction in GCLC language

dim 120 120

point H_{a} 80 40
point H 80 72.73

color 220 0 0
fontsize 11

cmark_b H_{a}
cmark_rt H
color 0 0 0
fontsize 10


% point B is given by the problem setting, but it has to belong to the line a which is constructible from the others objects given 
% DET:  points H_{a} and H are not the same
% Constructing a line h_{a} which passes through point H_{a} and point H
line h_{a} H_{a} H 

color 200 200 200
drawline h_{a}
color 0 0 0




% Constructing a line a which is perpendicular to line h_{a} and which passes through point H_{a}
perp a H_{a} h_{a} 

color 200 200 200
drawline a
color 0 0 0




% Constructing a point P_{\_G31590} with coordinates (10,30)
point P_{\_G31590} 10 30 
cmark_r P_{\_G31590}

% Constructing a line L_{\_G31593} which passes through point H and point H_{a}
line L_{\_G31593} H H_{a} 

color 200 200 200
drawline L_{\_G31593}
color 0 0 0


% Constructing a line L_{\_G31596} which is perpendicular to line L_{\_G31593} and which passes through point H_{a}
perp L_{\_G31596} H_{a} L_{\_G31593} 

color 200 200 200
drawline L_{\_G31596}
color 0 0 0


% Constructing a line L_{\_G31599} which passes through point H and point P_{\_G31590}
line L_{\_G31599} H P_{\_G31590} 

color 200 200 200
drawline L_{\_G31599}
color 0 0 0


% Constructing a point B which belongs to line L_{\_G31599} and line L_{\_G31596}
intersec B L_{\_G31599} L_{\_G31596} 
color 220 0 0
fontsize 11
cmark_b B
color 0 0 0
fontsize 10



% DET:  points B and H are not the same
% Constructing a line h_{b} which passes through point B and point H
line h_{b} B H 

color 200 200 200
drawline h_{b}
color 0 0 0




% Constructing a point A such that H_{a}A/H_{a}H=0.16956270420975122
towards A H_{a} H 0.16956270420975122 
cmark_t A
color 200 200 200
drawsegment H_{a} H 
color 0 0 0



% Constructing a point M_{c} such that AM_{c}/AB=0.5
towards M_{c} A B 0.5 
cmark_lt M_{c}
color 200 200 200
drawsegment A B 
color 0 0 0


% NDG:  points A and M_{c} are not the same
% Constructing a circle k(M_{c},A) whose center is at point M_{c} and which passes through point A
circle k(M_{c},A) M_{c} A 

color 200 200 200
drawcircle k(M_{c},A)
color 0 0 0



% NDG:  line h_{b} and circle k(M_{c},A) intersect% DET:  points B and H_{b} must be different
% Constructing a point P_{\_G19593} which is a foot of the point M_{c} on the line h_{b}
foot P_{\_G19593} M_{c} h_{b} 
cmark_r P_{\_G19593}
color 200 200 200
drawline M_{c} P_{\_G19593} 
color 0 0 0

% Constructing a point H_{b} which is an image of the point B in the symmetry to point/line P_{\_G19593}
sim H_{b} P_{\_G19593} B 
cmark_rt H_{b}


% DET:  points H_{b} and A are not the same
% Constructing a line b which passes through point H_{b} and point A
line b H_{b} A 

color 200 200 200
drawline b
color 0 0 0



% NDG:  lines a and b are not parallel% DET:  lines a and b are not the same
% Constructing a point C which belongs to line a and line b
intersec C a b 
cmark_b C



drawsegment A B
drawsegment A C
drawsegment B C

% Non-degenerate conditions:  lines a and b are not parallel; line h_{b} and circle k(M_{c},A) intersect; points A and M_{c} are not the same
% Determination conditions:  lines a and b are not the same; points H_{b} and A are not the same; points B and H_{b} must be different; points B and H are not the same; points H_{a} and H are not the same